PSI - Issue 5

L.F.P. Borrego et al. / Procedia Structural Integrity 5 (2017) 239–246 Borrego et al./ Structural Integrity Procedia 00 (2017) 000 – 000

241 3

10 -2

10 -3

10 -4

da /dN[mm/cycle]

10 -5

5

10

20 30

50 70

(a)

(b)

 K [MPa .m 0.5 ]

Fig. 1. (a) Geometry of CT specimen. (b) da/dN-  K plot in log-log scales.

3. Model to characterize the cyclic plastic deformation

3.1. Low cycle fatigue tests

Low-cycle fatigue tests were conducted on a DARTEC servo-hydraulic testing machine, equipped with a 100 kN load cell, at room temperature, and in laboratory air environment. The tests were conducted under axial total strain controlled mode, with sinusoidal waves, using a constant strain rate (da/dt) equal to 0.008 s-1, and total strain ratios (R  ) of -1 and total strain amplitude (  ) equal to 0.8%. Specimens were precisely produced according to the specifications outlined in ASTM E606 with a gage section measuring 25 mm in length and 6 mm in diameter specimens. The final surface finishing was obtained by high-speed mechanical polishing using different grades of silicon carbide papers (P600-grit, P1200-grit, and P2500-grit) followed by 3-  m diamond paste. A 12.5-mm strain gage extensometer was attached directly to the specimen gage section, using rubber bands, to evaluate the stress-strain relationship throughout the test. For each loading cycle, 200 samples were collected using a PC-based acquisition system. Figure 2 shows the stress-strain curve obtained. As can be noted, the material response is nearly stable. High precision in the numerical results generated by FEM, namely those of plastic CTOD, depends on the accurate modeling of the material elastic-plastic behavior. The elastic-plastic model adopted in this work assumes: (i) the isotropic elastic behavior modeled by the generalized Hooke’s law (the v alues of the elastic constants are shown in Table 2); (ii) the plastic behavior follows the von Mises yield criterion, coupled with Voce isotropic hardening law and Lemaître-Chaboche non-linear kinematic hardening law, under an associated flow rule. The von Mises yield surface is described by the equation: 3.2. Fitting of material constants